Question

9.
2. If the 4th term is 8 and the common
difference is -4, what are the first 3 terms
of the arithmetic sequence?
A. -4,0,4,8
B. -4,-8,4,8
C. 20, 16, 12,8
D. 20, 16,- 12,8​

Answer 1

Step-by-step explanation:

c. 16-20=-4

12-16=-4

8-12=-4

Answer 2

Answer :-

Option (C) 20,16,12,8

Explanation and Solution :-

Given :-

• $\mathtt{a_{4}} = 8$
• $\mathtt{common \: difference = - 4}$

$\underline{\bold{Let\: the\: 1st \: term \: be\: a}}$

$\: \: \: \: \: \: \: \: \boxed{ \bf\green{a_{n} = a + (n - 1)d}} \: \: \:$

$\: \: \: \: \: \sf{8 = a + (4 - 1) \times ( - 4) } \: \: \: \: \: \: \\ \: \: \: \: \: \sf{8 = a + 3 \times ( - 4) } \: \: \: \: \: \: \\ \: \: \: \: \: \sf{8 = a + ( - 12) } \: \: \: \: \: \: \\ \: \: \: \: \: \sf{ a =8 +12 } \: \: \: \: \: \: \\ \: \: \: \: \: \rightarrow\boxed{\sf{ a =20 }} \: \: \: \: \: \:$

Find 1st, 2nd, 3rd and 4th term

• $a_{1} = a, a_{2} =a_{1} - cd, a_{3}=a_{2}-cd, a_{4} = a_{3} - cd , so on$

then,

$\bf{\bold{a_{1} = \underline{20}} } \\ \bf{ \bold{a_{2} = 20-4 = \underline{16}}} , \\ \bf{ \bold{a_{3} = 16-4 = \underline{12}}} , \\ \bf{ \bold{a_{4} = 12-8 = \underline{8 }}}$

Option (C) is the right answer .

__________________________________

Extra information:-

Q) What is Arithmetic progression (AP) ?

A) Let say a, b, c an AP then difference between a b and bc are equal.

i.e, $\underbrace{a\leftrightarrow b}_{d} \: \underbrace{b\leftrightarrow c}_{d}$

$\boxed{a_{n} = a + (n-1) d}$

Where

• a = 1st term
• d= Common difference (cd)
• $a_{n}$ = nth term
• n = number of terms

#Gunjan